Determining Empirical
Formulas
Ck12 Science
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Printed: July 19, 2014
AUTHOR
Ck12 Science
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C HAPTER
Chapter 1. Determining Empirical Formulas
1
Determining Empirical
Formulas
• Define empirical formula.
• Calculate the empirical formula for a compound when given the elemental analysis of the compound.
What is occuring in this picture?
In the early days of chemistry, there were few tools for the detailed study of compounds. Much of the information
regarding the composition of compounds came from the elemental analysis of inorganic materials. The “new”
field of organic chemistry (the study of carbon compounds) faced the challenge of not being able to characterize a
compound completely. The relative amounts of elements could be determined, but so many of these materials had
carbon, hydrogen, oxygen, and possibly nitrogen in simple ratios. We did not know exactly how many of these
atoms were actually in a specific molecule.
Determining Empirical Formulas
An empirical formula is one that shows the lowest whole-number ratio of the elements in a compound. Because
the structure of ionic compounds is an extended three-dimensional network of positive and negative ions, all formulas of ionic compounds are empirical. However, we can also consider the empirical formula of a molecular
compound. Ethene is a small hydrocarbon compound with the formula C2 H4 (see Figure 1.1). While C2 H4 is its
molecular formula and represents its true molecular structure, it has an empirical formula of CH2 . The simplest
ratio of carbon to hydrogen in ethene is 1:2. There are two ways to view that ratio. Considering one molecule of
ethene, the ratio is 1 carbon atom for every 2 atoms of hydrogen. Considering one mole of ethene, the ratio is 1 mole
of carbon for every 2 moles of hydrogen. So the subscripts in a formula represent the mole ratio of the elements in
that formula.
In a procedure called elemental analysis, an unknown compound can be analyzed in the laboratory in order to
determine the percentages of each element contained within it. These percentages can be transformed into the mole
ratio of the elements, which leads to the empirical formula. The steps to be taken are outlined below.
1
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FIGURE 1.1
Ball-and-stick model of ethene, C2 H4 .
1. Assume a 100 g sample of the compound so that the given percentages can be directly converted into grams.
2. Use each element’s molar mass to convert the grams of each element to moles.
3. In order to find a whole-number ratio, divide the moles of each element by whichever of the moles from step
2 is the smallest.
4. If all the moles at this point are whole numbers (or very close), the empirical formula can be written with the
moles as the subscript of each element.
5. In some cases, one or more of the moles calculated in step 3 will not be whole numbers. Multiply each of the
moles by the smallest whole number that will convert each into a whole number. Write the empirical formula.
Sample Problem One: Determining the Empirical Formula of a Compound
A compound of iron and oxygen is analyzed and found to contain 69.94% iron and 30.06% oxygen.
empirical formula of the compound.
Step 1: List the known quantities and plan the problem.
Known
• % of Fe = 69.94%
• % of O = 30.06%
Unknown
• Empirical formula = Fe? O?
Steps to follow are outlined in the text.
Step 2: Calculate.
1. Assume a 100 g sample.
69.94 g Fe
30.06 g O
2. Convert to moles.
1 mol Fe
= 1.252 mol Fe
55.85 g Fe
1 mol O
30.06 g O ×
= 1.879 mol O
16.00 g O
69.94 g Fe ×
2
Find the
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Chapter 1. Determining Empirical Formulas
3. Divide both moles by the smallest of the results.
1.252 mol Fe
= 1 mol Fe
1.252
1.879 mol O
= 1.501 mol O
1.252
4/5. Since the moles of O, is still not a whole number, both moles can be multiplied by 2, while rounding to a whole
number.
1 mol Fe × 2 = 2 mol Fe
1.501 mol O × 2 = 3 mol O
The empirical formula of the compound is Fe2 O3 .
Step 3: Think about your result.
The subscripts are whole numbers and represent the mole ratio of the elements in the compound. The compound is
the ionic compound iron(III) oxide.
Summary
• A process is described for the calculation of the empirical formula for a compound based on the percent
composition of that compound.
Practice
Use the link below to read about calculating empirical formulas and practice working some problems:
http://www.chemteam.info/Mole/EmpiricalFormula.html
Review
Questions
1. What is an empirical formula?
2. What does an empirical formula tell you?
3. What does it not tell you?
• elemental analysis: Determines the percentages of each element in a compound.
• empirical formula: Shows the lowest whole-number ratio of the elements in a compound.
References
1. Harriet Moore. http://commons.wikimedia.org/wiki/File:M_Faraday_Lab_H_Moore.jpg .
2. Ben Mills (Wikimedia: Benjah-bmm27). http://commons.wikimedia.org/wiki/File:Ethylene-CRC-MW-3Dballs.png .
3